IndisputableMonolith.Physics.Structural_Physics_mod96
Structural physics certificate layer for a mod-96 domain cost built from the RS J-cost. Defines a nonnegative domain cost, a positive canonical threshold, and an inhabited certificate bundle packing those facts. Physicists citing structural selection or threshold comparisons in the RS physics stack would land here. Mostly definitional packaging plus elementary nonnegativity and positivity lemmas over Cost and Constants.
claimThe module introduces a domain cost $C_{\mathrm{dom}}$ derived from the RS cost $J$, proves $C_{\mathrm{dom}}\ge 0$ and an evaluation identity, fixes a canonical threshold $\theta>0$, and packages these into an inhabited structural-physics certificate $\mathrm{StructPhysicsM96Cert}$.
background
Recognition Science measures mismatch with the unique cost $J(x)=(x+x^{-1})/2-1$ forced by the Recognition Composition Law (T5). The Cost import supplies that $J$-calculus; Constants supplies the RS-native units and the time quantum $\tau_0=1$ tick.
This module sits in the Physics domain and builds a structural layer on top of those primitives. Sibling names indicate a domain-level cost functional, its pointwise evaluation identity, nonnegativity, a positive canonical threshold, and a certificate record that bundles the structural claims for downstream physics arguments.
The "mod96" tag marks a discrete structural bookkeeping scale used in the RS physics stack (certificate packaging rather than a new dynamical law).
proof idea
Definition-and-certificate module, not a deep derivation. Domain cost is defined from the imported $J$-cost; nonnegativity and the evaluation identity are short lemmas over Cost. The canonical threshold is a positive constant definition with a positivity proof. The certificate type and its inhabited instance simply assemble those facts into a single structural witness.
why it matters in Recognition Science
Gives the Physics stack a reusable structural certificate (domain cost, threshold, nonnegativity) so later selection or comparison arguments need not rebuild the $J$-based bookkeeping. No downstream edges are recorded on this page yet; the natural consumers are structural-physics theorems that quote an inhabited $\mathrm{StructPhysicsM96Cert}$ rather than re-proving cost positivity. Ties to the RS cost layer (T5 $J$-uniqueness) and the Constants spine, not to the forcing chain steps T6--T8 directly.
scope and limits
- Does not derive $J$ or the Recognition Composition Law; imports Cost.
- Does not force $\varphi$, eight-tick structure, or $D=3$.
- Does not compute particle masses, $\alpha$, or continuum field equations.
- Does not claim dynamical evolution; only structural cost and threshold facts.
- Does not list downstream consumers on this page (used_by empty).